Reconstruction of Time from RG Invariants

We demonstrate that physical time is not a fundamental background parameter, but a derived functional of renormalization group (RG) invariants. Defined on the space of quantum field theories equipped with the Zamolodchikov metric, we construct the RG-time functional as the normalized geodesic length of RG trajectories in theory space. We prove monotonicity via the 4D a-theorem, recover Friedmann equations as a projection of RG geometry, encode black hole entropy as a non-Markovian memory integral, and resolve the Wheeler-DeWitt frozen-time problem. This framework provides a complete ontological inversion: spacetime geometry becomes derived from the structure of theory space, with time as its intrinsic measure.